COMPASS: Composable Policy-Amortized Structured Search for LLM-Based Optimization Modeling

Large language models offer a promising technique for translating natural-language optimization problems into solver code, but their reliability remains constrained by the quality of template retrieval. While recent structured methods improve over flat prompting through hierarchical taxonomy search, their traversal rules remain fixed or LLM-driven at inference time, leaving retrieval unable to improve from past successes and failures. This motivates treating template retrieval as a policy that can be learned from modeling experience, rather than as a static inference-time rule. We propose COMPASS, a policy-amortized framework for retrieving optimization templates in LLM-based solver modeling, which represents the template library as a directed acyclic graph and formulates retrieval as a sequential decision process over template nodes. A deep Q-network learns a reusable traversal policy from template-level judgments and execution feedback, reducing reliance on fixed heuristic traversal through feedback-driven graph navigation. To support extensible retrieval, COMPASS embeds problem descriptions and template nodes in a shared semantic space, allowing newly inserted templates to be scored from their text descriptions without redefining the action space. Experiments across multiple LLM backbones and optimization-modeling benchmarks demonstrate that COMPASS consistently improves over heuristic structured retrieval, with the largest gains on complex and mixed-category problems.